In this paper we generalize Jacobsons results by proving that any integer  in   is a square-free integer), belong to . All units of  are generated by the fundamental unit  having the forms

our generalization build on using the conditions

This leads us to classify the real quadratic fields  into the sets  Jacobsons results shows that  and Sliwa confirm that  and  are the only real quadratic fields in .

The international reporting auditor witness rapidly developed over the past years, where profession began give attention to the development of auditor reporting and improve its informational report through the issuance and amendment of some relevant international auditing standards. The reality of the situation refers to the failure to inform the auditor in Iraq in  many areas, including: Clearly defined management responsibility for the preparation of financial and auditor's responsibility to express an opinion on these statements and Amendment of opinion when the financial statements as a whole is free from material misstatement based on the evidence is sufficient and appropriate audit, or not to build the auditor's ability to obt

The MTS-88. c trainer is a training system targeting students in the microprocessors course. It has a built in single-line assembler allowing the users to enter programs in assembly. It has the problem that long programs cannot be traced and tested efficiently. A simple error may cause all the code to be erased and the system to stop responding. Also, this system lacks the ability to be connected to the PC. The aim of this work is to modify the system to make it possible to be connected to the PC through the parallel port. This gives the capability to download long programs to the system after being developed in the PC. The 8255 Programmable Peripheral Interface available in the teaching system is interfaced to the parallel port and used as

English teachers in Iraq and other countries around the world up to this time use traditional methods to help students memorize new vocabularies. The sense of words or structure is not to be given in either the native tongue or the target language by definition, but is induced by the way the form is used in the situation. Situational Language Teaching (SLT) has recently become the needed method for improving speaking skills. It indicates the application of learning the language in actual and social exchange expressions so as to let learners do as required in classroom and non-classroom circumstances. This pilot study seeks to answer the following questions: Can SLT improve English speaking skills of target learners? How SLT contribute to th

Complex-valued regular functions that are normalized in the open unit disk are vastly studied. The current study introduces a new fractional integrodifferential (non-linear) operator. Based on the pre-Schwarzian derivative, certain appropriate stipulations on the parameters included in this con-structed operator to be univalent and bounded are investigated and determined.

When searching for an answer to the following question: What are the reasons for the reluctance of female physical education teachers in secondary schools to referee sports competitions according to the variable of years of service? It was found that the research aimed to reveal the differences between the opinions of the research sample of physical education teachers in secondary schools (girls) about refereeing sports competitions according to the variable of years of service. To achieve the research goal, it is assumed that there are significant differences between the average opinions of the research sample of female teachers and their reluctance and the reasons for the differences in the practice of refereeing sports competitions accor

Each sport has its own energy requirements that differ from the energy requirements of other sports, and a different method is used in each of them, so the trainer must first rely on the principle of privacy in training first, that is, privacy according to the working energy system, that is, he defines the controlling energy system In that event, and how the muscles use the available energy to perform according to the energy production systems. As we find the serving skill is the first volleyball skill with which the team starts the match in order to be able to gain points directly, through knowledge it turns out that there is a weakness in the skill performance, especially the skill of serving and being The key to victory for volle